Ever Heard of Heuristic Math? Here Are the Details
The very name "Math" denotes many things. For some, it is an emotion, a feeling, and a passion. For many, it is a nightmare and a challenge. Whatever the connection towards Math, the subject is inevitable in school life.
Math education is forever evolving. Since there is always room for improvement, mathematicians worldwide develop strategies and theories. Modern math requires far better problem-solving skills than what one normally has. School children often struggle with the subject when simple arithmetic exercises become complex Math problems.
Here is the solution! Introducing Math Heuristics. Heuristics are simple shortcuts and solutions used to solve Math problems. Problem-solving skills are fundamental to learning Math, so heuristics play a significant role in this subject. Heuristics reduce the number of mental operations students use to solve a Math problem and arrive at a solution.
Why Do School Children Need Math Heuristics?
School Math has evolved, and how! The Math taught in schools is very complex and demands high-order thinking. In Singapore, Math as a subject in school, for example, involves plenty of problem-solving, which can be fun and rewarding for some students and extremely challenging for others. Unlike simple Arithmetic, PSLE Math concepts require more aptitude to understand the question and figure out the approaches to find the solution. Besides, as children move to higher grades, Math only gets tougher. This is where heuristics can lend a helping hand, especially for children who struggle with the subject.
Math heuristics can:
- Improve problem-solving performance
Knowing a set of Math heuristics is a big advantage. It gives your child that extra edge and polishes their problem-solving skills. Think about the many times your child has struggled to get past a couple of steps to solve a Math problem. Here's where knowledge of heuristics makes a difference. Children are no longer intimidated by the problem. Instead, heuristics give them a confident start and guides their thinking process.
- Reduce effort and time
Heuristics in Math is all about using a systematic method to solve problems. Since most of them are tried and tested strategies, there is no need to derive a fresh one from scratch. All your child needs to do is apply the right heuristics to the right problem and find the solution.
Since Mathematics places problem-solving at its heart, using heuristics is inevitable.
A general heuristic may comprise the following protocol:
- Read the problem.
- Highlight the key points.
- Solve the problem.
- Recheck the work.
Many such heuristics are based on trial and error, rule of thumb, an educated guess, common sense, etc. However, Singapore's Ministry of Education (MoE) and the Curriculum Planning and Development Division (CPDD), the governing bodies that have devised the Singapore Math syllabi for PSLE, have identified 13 heuristics applicable for PSLE Math topics. Let's explore them.
Also Read : Ways to Revise for PSLE Maths
List of Heuristics to Solve Math PSLE Questions
The thirteen heuristics applicable for Math, as listed by the MoE and CPDD, are:
- Use equations
- Solve a part of the problem.
- Think of a related problem.
- Describe the problem in an alternative way.
- Make a systematic list.
- Act it out.
- Use the guess-and-check method.
- Work backwards.
- Use the before-after concept.
- Use suppositions.
- Work in reverse.
- Draw a diagram or model.
- Simplify the problem.
Based on their applications, these thirteen heuristics are divided into four categories. Based on the given problem, these applications help:
1. To represent
Visualise a problem, draw a diagram, make a list, and use equations to solve the problem.
2. To guess
Use guess-and-check suppositions, and look for patterns.
3. To process
Go through the process by acting it out, using before-after, and working backwards.
4. To alter
Change the problem by restating, simplifying, and solving a part of it.
How do heuristics help in solving a challenging Math problem?
Let's make one aspect very clear: Heuristics can enhance your child's problem-solving chances. However, there is no guarantee that they can definitely find the solution. There can be more than one way of solving the problem and finding the answer. This is true for complex problems that require multiple heuristic strategies.
The trick to using heuristics is to find the most suitable one that will help move from one step to another and eventually arrive at the solution. Mastering this art lies in how heuristics are taught, learnt, and applied. But "heuristics" itself cannot be only taught in class. Sometimes heuristics is taught by teachers, and sometimes, children learn it independently.
Besides, there are no hard and fast rules for teaching Math heuristics. It can be taught in the most unconventional methods, which we explain in our next segment.
3 Effective Ways to Teach & Learn Math Heuristics
1. Teaching and learning through play
Officially termed "Heuristic Play", this method opens up a world of unlimited discovery and applies to children as young as 18 months. This is when children develop an interest in toys, games, and their environment. They see new things, develop fresh connections, and generate new ideas and ways of doing things.
Heuristic play is the most simple and inexpensive method of developing your child's problem-solving skills. Children can use:
- Treasure baskets
- Tangram puzzles
- Stacking objects
- Furry objects
- Assortment of sea shells, plastic rings, hair rollers, etc
2. Learning through observation
Another effective method is watching and learning how others are solving problems and analysing if these methods are effective and practical. This method is the best way to understand that there is more than one approach to finding a solution. Teaching Heuristics through observation can help children become:
- More flexible in their thought process
- More competent in finding a solvable approach
It also helps them:
- Develop their reasoning on how and why to use strategies.
- Improve their confidence and open-mindedness about using heuristics.
3. Learning through discussion
When children discuss their approach to solving the problem with their peers, parents, or teachers, it gives them various insights and perspectives. Sharing a problem may help them find several easier alternatives. Moreover, it becomes easier to evaluate a problem-solving method when one uses verbalising to make one's thinking visible.
Win With Math Heuristics!
Heuristics and skills for problem-solving are essential to mathematics. Make sure your child uses Math Heuristics that are most appropriate for each scenario when solving the questions. Your child will see mathematical problems in a completely different light with these heuristics, increasing thier efficiency in problem-solving.
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